Verified answer

I think it is correct. I would use 'to' in place of 'ni' (name) san to yoku hanashite... I am not quite sure why. I am wondering if by using 'ni' that you talk "at" somebody rather than "with" them as 'to' indicates. A second point that concerns me is the use of kara with the -te form. this means "after" as in "after talking with..." I would have to do a lot of research to confirm my suspicion that "since" and "after" are different in Japanese. Finally "has been improving" why not 'joutatsu shite iru?' I would have to get a bunch of books out to check up on the meaning of saseru. I see this construction often. I am just wondering if that is what mean to say ( he he not knowing what exactly the meaning is at present).

Anyway, it is more or less the case of the blind leading the blind. Maybe a one-eyed man will come along and set it all straight.

I think hirame explained well.

(name)さんとよく話したから、私の日本語は上達しつつあります

or

(name)さんとよく話したから、私の日本語は上達しているところです

But, "しつつあります" and "しているところです" aren't used so often. We usually say just "上達しました"(my Japanese was improved).